Question

Find the equation of the circle with radius $5$ whose center lies on the x-axis and passes through the point $(2, 3).$

Answer 1

Let the equation of the required circle be $(x - h)^2 + (y - k)^2 = r^2.$
Since the radius of the circle is 5 and its center lies on the x-axis, $k = 0$ and $r = 5$. Now, the equation of the circle becomes $(x - h) ^2 + y^2 = 25.$
It is given that the circle passes through points $(2, 3).$

$(2 – h)^2+ 32 = 25$

$(2 – h)2 = 25-9$

$(2 – h)^2 = 16$$$

$2 – h = ± √16 = ± 4$$$

If $2-h = 4,$ then $h = -2$ (Ans.)